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The number 153 is associated with the geometric shape known as theVesica piscis or Mandorla.Archimedes, in hisMeasurement of a Circle, referred to this ratio (153/265), as constituting the "measure of the fish", this ratio being an imperfect representation of $1/{\sqrt {3}}\approx 0.57735$ .^[2]

As atriangular number, 153 is the sum of the first17 integers, and is also the sum of the first five positivefactorials: $1!+2!+3!+4!+5!$ .^[1]

The number 153 is also ahexagonal number, and a truncated triangle number, meaning that 1, 15, and 153 are all triangle numbers.

The distinct prime factors of 153 add up to 20, and so do the ones of 154, hence the two form aRuth-Aaron pair.

Since $153=1^{3}+5^{3}+3^{3}$ , it is a 3-narcissistic number, and it is also the smallest three-digit number which can be expressed as the sum of cubes of its digits.^[3] Only five other numbers can be expressed as the sum of the cubes of their digits:0,1, 370, 371 and 407.^[4] It is also aFriedman number, since 153 = 3 × 51.

TheBiggs–Smith graph is asymmetric graph with 153 edges, all equivalent.

Another feature of the number 153 is that it is the limit of the following algorithm:^[5]^[6]^[7]

Take a random positiveinteger, divisible bythree
Split that number into its base 10 digits
Take the sum of their cubes
Go back to the second step

An example, starting with the number84:

${\begin{aligned}8^{3}+4^{3}&=&512+64&=&576\\5^{3}+7^{3}+6^{3}&=&125+343+216&=&684\\6^{3}+8^{3}+4^{3}&=&216+512+64&=&792\\7^{3}+9^{3}+2^{3}&=&343+729+8&=&1080\\1^{3}+0^{3}+8^{3}+0^{3}&=&1+0+512+0&=&513\\5^{3}+1^{3}+3^{3}&=&125+1+27&=&153\\1^{3}+5^{3}+3^{3}&=&1+125+27&=&153\end{aligned}}$

There are 153uniform polypeta that are generated from four different fundamentalCoxeter groups in six-dimensional space.

The sum of the first eightHeegner numbers is 153.

In the Bible

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*Appearance on Lake Tiberias* byDuccio, 14th century, showingJesus and the 7 fishing disciples (withSaint Peter leaving the boat)

TheGospel of John (chapter 21:1–14) includes themiraculous catch of 153 fish as the third appearance of Jesus after hisresurrection.^[8]Augustine of Hippo argued that the significance lay in the fact that 153 is the sum of the first 17integers (i.e. 153 is the 17thtriangular number), representing the combination ofdivine grace (theseven gifts of the Holy Spirit) and law (theTen Commandments).^[9]

References

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^^a ^bWells, D.The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140–141.
^"Measure of the Fish".greatdreams.com.
^Gupta, Shayam Sunder."Curious Properties of 153". RetrievedJune 26, 2009.
^OEIS:A046197
^Catch of the Day (153 Fishes) at mathpages.com.
^OEIS:A165330
^OEIS:A346630
^Biblegateway John 21:1–14
^Jason Byassee,Praise Seeking Understanding: Reading the Psalms with Augustine, Wm. B. Eerdmans Publishing, 2007, p. 130,ISBN 0-8028-4012-4.

Bibliography

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Twelftree, Graham H. (1999). "Miracles in the Fourth Gospel".Jesus the Miracle Worker: A Historical and Theological Study. InterVarsity Press.ISBN 9780830815968.
Flanagan, Neal M. (1992). "John". In Karris, Robert J. (ed.).The Collegeville Bible Commentary: Based on the New American Bible. Liturgical Press.ISBN 9780814622117.
Edwards, Mark (2008).John Through the Centuries. Wiley Blackwell Bible Commentaries. John Wiley & Sons.ISBN 9781405143196.
Culpepper, R. Alan (2021).Designs for the Church in the Gospel of John: Collected Essays, 1980–2020. Wissenschaftliche Untersuchungen zum Neuen Testament. Vol. 465. Mohr Siebeck.ISBN 9783161602627.
Bernard, John Henry (1928). "Introduction".A critical and exegetical commentary on the Gospel According to St John. Vol. 1. Edinburgh: ICC.ISBN 9780567050243.{{cite book}}:ISBN / Date incompatibility (help)
Bernard, John Henry (1928). "Notes on the Greek text".A critical and exegetical commentary on the Gospel According to St John. Vol. 2. Edinburgh: ICC.ISBN 9780567050243.{{cite book}}:ISBN / Date incompatibility (help)
Grant, Robert M. (2002). "Unusual animals".Early Christians and Animals. Routledge.ISBN 9781134633753.
Manning, Gary T. Jr. (2004).Echoes of a Prophet: The Use of Ezekiel in the Gospel of John and in Literature of the Second Temple Period. The Library of New Testament Studies. Vol. 270. A&C Black.ISBN 9780567639288.
Godet, Frédéric Louis;Dwight, Timothy (1893).Commentary on the Gospel of John, with an Historical and Critical Introduction. New York: Funk & Wagnalls.
Wiarda, Timothy James (1992). "John 21.1–23: Narrative Unity and Its Implications".Journal for the Study of the New Testament.14 (6):53–71.doi:10.1177/0142064X9201404604.S2CID 145428133.
Keener, Craig S. (2010). "Epilogue (21:2–25)".The Gospel of John. Baker Academic.ISBN 9781441237057.
Hunter, Archibald Macbride (1965). Hunter, Alan (ed.).The Gospel According to John. Cambridge Bible Commentaries on the New Testament. Cambridge University Press.ISBN 9780521092555.

External links

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The Number 153 at The Database of Number Correlations Archived March 20, 2014, at theWayback Machine

v
t
e

\mathbb {Z}

Integers

−2,−1

0 to 199

0 to 99	100 to 199
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99	100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

200 to 399

200 to 299	300 to 399
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299	300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 318 323 325 341 353 359 360 363 365 369 377 384

400 to 999

400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2520 3000 3511 4000 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

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